Lyon claimed nine maidens from his 24 overs on the day and only conceded 40 runs, leading Pietersen to say England were too negative in their approach.
‘One thing I would say is that Nathan should not bowl 24 overs for 40 runs on day one of a Test match,’ he told BT Sport.
‘They’ve missed a trick there. I would have preferred Lyon’s figures to have been 3-80.
‘You get defined as a player with the risks you take, you’re going to have to take risks as a top-order batsman. You want to stand out but they’ve done a job.’
Lloyd says his ‘only concern’ after an encouraging day for the tourists was the way in which they played 30-year-old Lyon.
‘My only concern with how England played was that they showed too much respect to Nathan Lyon,’ Bumble told the Daily Mail.
‘Going at two and a half runs an over is too slow.
‘With Australia fielding four bowlers you have to be proactive against their spinner to make Steve Smith use his quicks. You want to be on about 270 when the second new ball comes.’
Ex-England head coach Lloyd added: ‘Make no mistake, our lads can play. I have said consistently that the pitches we saw in England in the summer were not straightforward.
‘Pitches in Australia will be and players like James Vince, Dawid Malan and Mark Stoneman will find it easier. Their strong performances didn’t surprise me.’